Question

Sin theter over Cos theter x 1 over Tan theter = 1​

Answer 1

Answer and Explanation:

`(\sin(\theta))/(\cos(\theta)) \cdot (1)/(\tan(\theta)) = 1`

In this problem, we need to verify the identity using the given equation.

First, rewrite tangent using its definition.

`\tan(\theta) = (\sin(\theta))/(\cos(\theta))`

`(\sin(\theta))/(\cos(\theta)) \cdot (1)/((\sin(\theta))/(\cos(\theta))) = 1`

Next, simplify the fraction on the right.

`(\sin(\theta))/(\cos(\theta)) \cdot (\cos(\theta))/(\sin(\theta)) = 1`

Finally, cancel the cosine and sines in the numerator and denominator.

`\frac{\\ot{\cos(\theta)} \cdot \\ot{\sin(\theta)}}{\\ot{\cos(\theta)} \cdot \\ot{\sin(\theta)}} = 1`

`1 = 1`